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Generalized dromion solutions of a new higher dimensional soliton equation

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Communications in Nonlinear Science and Numerical Simulation 2001年第2期6卷 97-101页

作者： Jiefang ZHANG and Gongdi XU Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China College of Chemical Engineering, Qiqihar University, Qiqihar 161 Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China Institute of Nonlinear Physics Zhejiang Normal University Jinhua 321004 China College of Chemical Engineering Qiqihar University Qiqihar161000 China

We derive the generalized dromions of the new higher dimensional soliton equation by suitably utilizing the arbitrary function present in the bilinearized linear equations. The rich dromion structures for this system ... 详细信息

关键词： dromion soliton equation

On a Formation of Singularities of Solutions to soliton equations Represented by L,A,B-triples

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Acta Mathematica Sinica,English Series 2024年第1期40卷 406-416页

作者： Iskander A.TAIMANOV Novosibirsk State University 630090 Novosibirskand Sobolev Institute of Mathematics630090 NovosibirskRussia

We discuss the mechanism of formation of singularities of solutions to the Novikov-Veselov,modified Novikov-Veselov,and Davey-Stewartson II(DSII)equations obtained by the Moutard type *** equations admit the L,A,B-triple presentation,the generalization of the L,Apairs for 2+1-soliton *** relate the blow-up of solutions to the non-conservation of the zero level of discrete spectrum of the *** also present a class of exact solutions,of the DSII system,which depend on two functional parameters,and show that all possible singularities of solutions to DSII equation obtained by the Moutard transformation are indeterminancies,i.e.,points when approaching which in different spatial directions the solution has different limits.

关键词： soliton equation blow up Davey-Stewartson equation Moutard transformation

THE INTEGRABILITY AND PARAMETRIC REPRESENTATION OF A HIERARCHY OF soliton equationS

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Acta Mathematicae Applicatae Sinica 2001年第3期17卷 310-316页

作者：张磊施齐焉 Department of Mathematics Zhongshan University Guangzhou China Department of Mathematics Peking University Beijing China

The parametric representation for finite-band solutions of a stationary soliton equation is discussed. This parametric representation can be represented as a Hamiltonian system which is integrable in Liouville sense. The nonconfocal involutive integral representations {Fm} are obtained also The finite-band solutions of the soliton equation can be represented as the solutions of two set of ordinary differential equations.

关键词： soliton equation Hamiltonian system Liouvill integrable finite-band solution

Lump solutions to a generalized Hietarinta-type equation via symbolic computation

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Frontiers of Mathematics in China 2020年第3期15卷 435-450页

作者： Sumayah BATWA Wen-Xiu MA Department of Mathematics King Abdulaziz UniversityJeddahSaudi Arabia Department of Mathematics Zhejiang Normal UniversityJinhua 321004China Department of Mathematics and Statistics University of South FloridaTampaFL 33620USA School of Mathematics South China University of TechnologyGuangzhou 510640China

Lump solutions are one of important solutions to partial differential equations,both linear and *** paper aims to show that a Hietarinta-type fourth-order nonlinear term can create lump solutions with second-order linear dispersive *** key is a Hirota bilinear *** solutions are constructed via symbolic computations with Maple,and specific reductions of the resulting lump solutions are *** illustrative examples of the generalized Hietarinta-type nonlinear equations and their lumps are presented,together with three-dimensional plots and density plots of the lump solutions.

关键词： soliton equation lump solution symbolic computation Hirota derivative dispersion relation

Linear superposition of Wronskian rational solutions to the KdV equation

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Communications in Theoretical Physics 2021年第6期73卷 1-5页

作者： Wen-Xiu Ma Department of Mathematics Zhejiang Normal UniversityJinhua 321004ZhejiangChina Department of Mathematics King Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics and Statistics University of South FloridaTampaFL 33620-5700United States of America School of Mathematical and Statistical Sciences North-West UniversityMafikeng CampusPrivate Bag X2046Mmabatho 2735South Africa

A linear superposition is studied for Wronskian rational solutions to the Kd V equation,which include rogue wave *** is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear Kd V *** is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.

关键词： soliton equation Wronskian solution rational solution rogue wave the KdV equation

SOLVING AKNS equationS VIA JACOBI INVERSION PROBLEM

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Acta Mathematicae Applicatae Sinica 1999年第4期15卷 337-344页

作者：曾云波 Department of Mathematical Sciences Tsinghua University Beijing China

By using Lax representation, we study the separation of variables for x- and tn-finitedimensional integrable Hamiltonian system (FDIHS) obtained from the factorization of AKNShierarchy. Then the separability of X- and tn-FDIHS and the factorization of AKNS hierarchy give rise to the Jacobi inversion problem for soliton equations in AKNS hierarchy. By a standard Jacobi inversion technique, the soliton equations can be solved in terms of Riemann theta function.

关键词： Separation of variables Jacobi inversion problem soliton equation factorization

LAX REPRESENTATIONS FOR DIRAC soliton HIERARCHY

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Annals of Differential equations 1998年第1期14卷 76-80页

作者：伍泳棠朱思铭施齐焉中山大学

This paper obtains Dirac soliton hierarchy and their Lax representations from a eigenvalue problem. The corresponding Lenard's recursive sequence can be solved explicitly.

关键词： eigenvalue problem soliton equation Lax representation